Very cool that air can be 'melted' into a conducting state.
[Edit: reading further I see Bill is onto a similar line of thought.]
Let's try this. Say a mast is grounded to sea water and therefore at the potential of the seawater, call it arbitrarily zero. Let's say the mast is in the uniform field you described above. Now flip a switch that disconnects the ground and isolates the mast from the seawater. What is the potential of the mast? If it changed, how does that happen? Is it instantaneous, or does it develop over time? Is a finite derivative for potential possible without an associated current? If you float the mast up 1000ft and connect an insulated perfect conductor to it back to the boat, could you use the wire like one terminal of a battery? The problem I'm having is that potential is not a state variable. Potential is the, well, potential for work to be done, in this case by an electric field. The field depends on charge distribution. So if the charge distribution in the mast is not changing, how does its potential change such that it comes to an equipotential value that is the average field value in the air along its length?Regarding this
If there is no current flowing in a good conductor - the field across it is zero (ohms law). If your mast is insulated by air from any source of current, it will have zero volts across it - and in an electric field, will take on the single potential of its mid point in the field.
[Edit: reading further I see Bill is onto a similar line of thought.]